Question: Simplify to lowest terms. $\dfrac{72}{84}$
Answer: There are several ways to tackle this problem. What is the greatest common factor (GCD) of 72 and 84? $72 = 2\cdot2\cdot2\cdot3\cdot3$ $84 = 2\cdot2\cdot3\cdot7$ $\mbox{GCD}(72, 84) = 2\cdot2\cdot3 = 12$ $\dfrac{72}{84} = \dfrac{6 \cdot 12}{ 7\cdot 12}$ $\hphantom{\dfrac{72}{84}} = \dfrac{6}{7} \cdot \dfrac{12}{12}$ $\hphantom{\dfrac{72}{84}} = \dfrac{6}{7} \cdot 1$ $\hphantom{\dfrac{72}{84}} = \dfrac{6}{7}$ You can also solve this problem by repeatedly breaking the numerator and denominator into common factors. For example: $\dfrac{72}{84}= \dfrac{2\cdot36}{2\cdot42}= \dfrac{2\cdot 2\cdot18}{2\cdot 2\cdot21}= \dfrac{2\cdot 2\cdot 3\cdot6}{2\cdot 2\cdot 3\cdot7}= \dfrac{6}{7}$